Examples with solutions for Subtraction: Graphical representation - subtraction with regrouping

Exercise #1

What do you get if you subtract 9 units from 27 units?

Step-by-Step Solution

To solve this problem, we need to subtract one number from another. Here's a step-by-step approach:

  • Identify the numbers: We need to subtract 9 units from 27 units.
  • Set up the subtraction operation: 279 27 - 9 .
  • Perform the subtraction: Subtracting 9 from 27 involves straightforward arithmetic:
    The operation is 279=18 27 - 9 = 18 .
  • Simplify: The difference calculated is 18.

Therefore, the result of subtracting 9 units from 27 units is 18 18 .

Answer

18 18

Exercise #2

What do you get if you subtract 9 units from 48 units?

Step-by-Step Solution

To solve this problem, we need to subtract 9 from 48. This involves simple subtraction:

  • Write the numbers vertically, aligning the decimal if necessary, though here they are whole numbers:
       48
    -
        9
  • We start from the rightmost column (units place). Subtract 9 from 8:
  • Since you cannot subtract a larger number from a smaller one without getting into negative numbers, you should consider regrouping.
  • We take 1 from the tens place, turning the 4 (in 48) to 3, and the 8 (becomes 18).
  • Subtract 9 from 18, which gives 9.
  • The remaining in tens column is 3 (because we reduced it by 1).

By combining these, the subtraction of 9 units from 48 units gives us:

39 39

Therefore, the solution to the problem is 39 39 , which matches the third choice given.

Answer

39 39

Exercise #3

What do you get if you subtract 8 units from 17 units?

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Identify the minuend and subtrahend.
  • Perform the subtraction operation.
  • Verify the result with the provided answer choices.

Now, let's work through each step:
Step 1: The given numbers are 17 (minuend) and 8 (subtrahend).
Step 2: Using the subtraction formula, we calculate 178=9 17 - 8 = 9 .
Step 3: Cross-reference the result with the provided answer choices to ensure it matches choice 4, which is 9.

Therefore, the solution to the problem is 9 9 .

Answer

9 9

Exercise #4

If we have 45 blocks in total and we remove 7 of those blocks, how many blocks remain?

Remember you can break down a row of 10 blocks into single units.

Step-by-Step Solution

To solve this problem, we'll adhere to a few simple steps:

  • Step 1: Identify the given numbers; initially, we have 45 45 blocks.
  • Step 2: Determine the number of blocks to remove, which is 7 7 .
  • Step 3: Subtract the removed blocks from the total: 457 45 - 7 .

Now, let's perform the calculation:
The difference between 45 45 and 7 7 can be found by performing the subtraction:
457=38 45 - 7 = 38 .

Therefore, after removing 7 7 blocks from 45 45 blocks, the number of blocks remaining is 38 38 .

Thus, the solution to the problem is 38 38 .

Answer

38 38

Exercise #5

If we have 72 blocks in total and we remove 4 of those blocks, how many blocks remain? Remember you can break down a row of 10 blocks into single units.

Step-by-Step Solution

To solve this problem, we will perform a simple subtraction of the number of removed blocks from the total number of blocks.

  • Step 1: Identify the total number of blocks and the blocks removed.
  • Step 2: Use the formula for subtraction to determine the remaining blocks: Remaining blocks=Initial blocksRemoved blocks \text{Remaining blocks} = \text{Initial blocks} - \text{Removed blocks} .
  • Step 3: Perform the calculation.

Now, let's work through each step:

Step 1: We start with 72 72 blocks and remove 4 4 blocks.

Step 2: Using the subtraction formula mentioned, we compute:
724=68 72 - 4 = 68 .

Step 3: Therefore, after removing 4 blocks, the number of blocks that remain is 68 68 .

Thus, the solution to the problem is 68\mathbf{68}.

Answer

68 68

Exercise #6

If we have 34 blocks and we remove 8 blocks, how many blocks will remain?

Step-by-Step Solution

To solve this problem, we'll carry out the following steps:

  • Step 1: Identify the total number of blocks initially present, which is given as 34.
  • Step 2: Identify the number of blocks to be removed, which is provided as 8.
  • Step 3: Use subtraction to calculate the remaining number of blocks after some have been removed.

Now, let's perform the calculation:

Starting with 34 blocks, and needing to remove 8 blocks, we calculate:

Remaining=348 \text{Remaining} = 34 - 8

Calculating this, we have:

348=26 34 - 8 = 26

Therefore, the number of blocks that will remain is 26 26 .

Answer

26 26

Exercise #7

If we have 48 blocks in total and we remove 19 of those blocks, how many blocks remain? Remember you can break down a row of 10 blocks into single units.

Step-by-Step Solution

To solve the problem of finding how many blocks remain after removing 19 from 48, we will perform the subtraction operation and handle regrouping if necessary:

Step 1: Start with the original number of blocks: 48 48 .

Step 2: We need to subtract 19 from this total. Let's write this subtraction vertically:

4819 \begin{array}{c} 48 \\ - 19 \\ \hline \end{array}

Step 3: In the units column (rightmost column), we have 8 (from 48) and we need to subtract 9. Since 8 is smaller than 9, we regroup from the tens column. This leaves us with:

  • Convert one 10 from the tens place in 48, leaving 3 tens, and add that 10 to the units column, making it 18.
  • Now subtract 9 from 18 in the units column. This results in 9.

Step 4: Proceed to the tens column. We regrouped once, so we're left with 3 tens (from original 4 tens). Subtract 1 ten (from the 19) from 3 tens, leaving us with 2 tens.

Thus, the remaining amount after performing the subtraction is:

381929 \begin{array}{c} 3 & 8 \\ - 1 & 9 \\ \hline 2 & 9 \\ \end{array}

Therefore, the number of blocks remaining is 29 \boxed{29} .

Answer

29 29

Exercise #8

If we have 17 blocks in total and we remove 14 of those blocks, how many blocks remain? Remember you can break down a row of 10 blocks into single units.

Step-by-Step Solution

We need to determine how many blocks are left after removing a certain number from a total.

First, let's identify the given figures:

  • Initial number of blocks: 17 17
  • Number of blocks removed: 14 14

The formula for finding out how many blocks remain is subtraction:

Remaining Blocks = Total Blocks - Blocks Removed

Substituting the given numbers into this formula:

Remaining Blocks = 1714 17 - 14

We perform the subtraction:

1714=3 17 - 14 = 3

Therefore, after removing 14 blocks from the total of 17, we find that the number of blocks remaining is 3\mathbf{3}.

Answer

3 3

Exercise #9

If we have 46 blocks in total and we remove 27 of those blocks, how many blocks remain? Remember you can break down a row of 10 blocks into single units.

Step-by-Step Solution

To solve this problem, let's follow a step-by-step approach using subtraction with regrouping:

  • Step 1: Set up the subtraction problem as 4627 46 - 27 .
  • Step 2: Compare the one's place: 6 (in 46) and 7 (in 27). Since 6 is less than 7, we need to regroup.
  • Step 3: Regroup one ten from the 4 tens in 46. This will leave us with 3 tens and increase the units to 16.
  • Step 4: Now perform the subtraction for the one's place: 167=9 16 - 7 = 9 .
  • Step 5: Subtract the tens: 32=1 3 - 2 = 1 .

Thus, the remaining number of blocks after removing 27 from 46 is 19 19 .

Answer

19 19

Exercise #10

If we have 72 blocks in total and we remove 45 of those blocks, how many blocks remain? Remember you can break down a row of 10 blocks into single units.

Step-by-Step Solution

To solve this problem, we'll perform a simple subtraction:

  • Step 1: Identify the given numbers: Total blocks = 72, Blocks to remove = 45.
  • Step 2: Subtract the number of blocks being removed from the total number of blocks.

Let's perform the subtraction step-by-step:

7245 72 - 45

First, subtract the units digit: 25 2 - 5 .

Since 2 is smaller than 5, we need to borrow from the tens column:

  • Borrow 1 ten from the 7 (in 72), making it 6.
  • The units now become 12.

Now subtract the units digits: 125=7 12 - 5 = 7 .

Next, subtract the tens digits: 64=2 6 - 4 = 2 .

Combine the results to get the number remaining:

The number of blocks remaining after removing 45 from 72 is 27 27 .

This matches the correct choice among the provided answers, which is option 3: 27 27 .

Therefore, the solution to the problem is 27 27 .

Answer

27 27

Exercise #11

If we have 53 blocks in total and we remove 38 of those blocks, how many blocks remain? Remember you can break down a row of 10 blocks into single units.

Step-by-Step Solution

Let's solve the subtraction problem to find out how many blocks remain:

Given:

  • Total number of blocks = 53 53
  • Number of blocks removed = 38 38

We need to perform the subtraction of 38 38 from 53 53 :

Set up the subtraction column:

  • 5835 \begin{array}{c} \phantom{-} 5\phantom{8} \\ - \, 3\phantom{5} \\ \hline \end{array} Tens digit (5) minus 3 is 2.
  • 2338 \begin{array}{c} \phantom{2}3 \\ - \phantom{3}8 \\ \hline \end{array} Units column requires borrowing: change 5 5 tens to 4 4 tens and add 10 to units.
  • 1131815 \begin{array}{c} \phantom{1}13 \\ - \phantom{1}8 \\ \hline \phantom{1}5 \end{array}

Final calculation gives 15 15 .

Therefore, the number of blocks remaining is 15 15 .

Answer

15 15

Exercise #12

If we have 34 blocks in total and we remove 16 of those blocks, how many blocks remain? Remember you can break down a row of 10 blocks into single units.

Step-by-Step Solution

First, we start with the total number of blocks, which is 34 34 .

We need to remove 16 16 blocks from this total. Therefore, we perform the subtraction:

3416 34 - 16 .

Let's break this down:
34 34 is composed of 3 3 tens (i.e., 30 30 ) and 4 4 ones.
Subtracting 16 16 means subtracting 1 1 ten and 6 6 from these 34 34 blocks.

First, subtract 10 10 from 34 34 , which leaves us with 24 24 . Then, subtract 6 6 from 24 24 , giving:

246=18 24 - 6 = 18 .

Therefore, after removing 16 16 blocks, we are left with 18 18 blocks.

The solution to the problem is 18 18 .

Answer

18 18

Exercise #13

If we have 27 blocks in total and we remove 18 of those blocks, how many blocks remain? Remember you can break down a row of 10 blocks into single units.

Step-by-Step Solution

To solve this problem, begin by employing the basic subtraction formula:

  • Subtract the blocks removed (18) from the total number of blocks (27).
  • Mathematically, this is written as: 2718 27 - 18 .

Perform the subtraction:

2718=927 - 18 = 9.

Therefore, the number of blocks remaining after removing 18 from 27 is 9\boxed{9}.

Answer

9 9